How do I add a red dot on a specific part of a 3D model?
Is the following what you're trying to do?

You have a material on your surface.  In Edit mode, cut new edges to define the area to be filled with red. In the picture below, I've moved vertices, but that'll muck up your UVs so just cut new edges without moving them.  Select the area to be assigned the Red Dot material. Create a new material slot by clicking on the + sign and create the red material. Click on Assign.  Then you can come out of Edit mode.